Explain Biot and Savart’s law with suitable diagram.

Answer: The magnetic field \(dB\) at a point due to a small current element \(I\,dl\) is \(dB = \dfrac{\mu_0}{4\pi}\dfrac{I\,dl\sin\theta}{r^2}\).

[Figure: a wire carrying current I; a small element dl on it; a point P at distance r from the element; θ is the angle between dl (in the direction of the current) and the line r joining the element to P. The field dB at P is perpendicular to the plane containing dl and r.]

According to Biot–Savart’s law, the magnitude of the magnetic induction \(dB\) at P is

• directly proportional to the current \(I\),
• directly proportional to the length \(dl\) of the element,
• directly proportional to \(\sin\theta\),
• inversely proportional to the square of the distance \(r\).

where \(\mu_0 = 4\pi\times10^{-7}\) Wb/A m. The direction of \(\vec{dB}\) is that of \(\vec{dl}\times\vec{r}\), given by the right-hand rule.